Ancient DNA analyses have transformed the research of human evolution, making it possible to directly reconstruct patterns of migrations and responses to natural selection. Key to these inferences is the reliable estimation of the age of the ancient samples. Radiocarbon dating, the standard tool used by archaeologists, suffers from many limitations; in particular, relying on knowledge of historical and geographic estimates of atmospheric carbon isotopes, which are hard or impossible to obtain. This proposal introduces two genetic approaches for dating ancient genomes, which capitalize on the insight that an ancient genome lacks several thousand years of evolution compared to the genomes of extant living individuals. Given a molecular clock provided by the steady accumulation of mutations or recombination events, one can thus infer the missing evolution or branch shortening. This branch shortening can be converted into an age in years given an estimate of the generation time or an independent calibration such as human-chimpanzee divergence. A major challenge of this approach is that when dating samples that are tens of thousands of years old or less, the branch shortening is extremely small compared to the total divergence to outgroups. As a solution, I propose to take advantage of the unique history of Neandertal gene flow that occurred ~50,000 years ago and contributed 1-4% ancestry to the genomes of most non-Africans. In these introgressed regions, Neandertal is a much closer outgroup to modern humans, allowing a more reliable estimate of the branch shortening. Specifically, I propose to develop two methods, based on mutation and recombination clocks respectively: (i) I will estimate the sequence divergence between Neandertals and both the ancient and extant genomes and the proportional reduction in the divergence in ancient genomes at Neandertal introgressed segments. Given an estimate of the mean human-Neandertal divergence time, I can then estimate the age of the ancient sample in years. (ii) Gene flow between genetically distinct populations creates correlation in ancestry across the genome that decays as a function of the time elapsed since the mixture and the recombination rate. Using this decay pattern, I will estimate the time of Neandertal gene flow for the ancient and extant samples. Using the difference in estimated dates and a human generation time estimate, I will infer the age of the ancient sample. These approaches provide a much-needed complement to existing dating methods and are applicable for dating samples that are tens of thousands of years old.